Speaker: Omkar Javadekar
Abstract: It is conjectured that the support of the local cohomology modules is closed. In this talk, we will present Hochster and Betanncourt's proof of this conjecture for hypersurface rings.
Time: 2:30 PM–3:30 PM
Venue: Ramanujan Hall
Speaker: Aditya Dwivedi
Abstract: The theorem of Kunz (1970) characterizes a ring as being regular in terms of the flatness of the Frobenius map. The theorem is widely considered as the first theorem in positive characteristic methods. We will see a proof of this fundamental theorem in this talk.
Time: 2 PM–3 PM
Venue: Ramanujan Hall
Speaker: Sayed Sadiqul Islam
Abstract: The title says it all. The prerequisite needed is basic commutative algebra. The talk is based on the following paper: D. Eisenbud, E.G. Evans Jr., "Every algebraic set in n-space is the intersection of n hypersurfaces", Invent. Math., 19 (1973), pp. 107–112.
Time: 4 PM–5 PM
Venue: Ramanujan Hall
Speaker: Soumyadeb Samanta
Abstract: Let us first recall the following theorem of Gromov : Every finitely generated group of polynomial growth is virtually nilpotent. As simple as the statement might look, the proof of this theorem is quite non-elementary; recently Bruce Kleiner gave an alternative proof of this result. Our aim in this talk is to discuss Kleiner's proof of Gromov's theorem assuming the proof of one of Kleiner's theorems. This talk will be made as self contained as possible.
Time: 5 PM–6 PM
Venue: Ramanujan Hall
Speaker: Pradip Kumar Maity
Abstract: I shall discuss about the Jacobi fields and see some examples of Jacobi fields of manifolds with constant curvature. Then we will see some comparison results such as the Cartan–Hadamard theorem.
Time: 4 PM–5 PM
Venue: Ramanujan Hall
Speaker: Aditya Dwivedi
Abstract: This talk will present the proof of the classical Erdős–Ko–Rado theorem. It is the oldest result in extremal combinatorics, and we present proof using the shifting method. Although proved by Erdős–Ko–Rado in 1938, it was not published till the 1960s because the authors found the theorem less interesting then.
Time: 4 PM–5 PM
Venue: Ramanujan Hall
Speaker: Om Milind Joglekar
Abstract: The Robinson–Schensted–Knuth (RSK) correspondence establishes a profound bijection between matrices of finite support and pairs of standard Young Tableaux of the same shape. A striking symmetry property of the RSK is that transposing a matrix swaps its resulting tableaux: if a matrix A corresponds to (P, Q), then Aᵀ corresponds to (Q, P). In this talk, I will present a proof of this elegant symmetry using the matrix-ball construction.
Time: 6 PM–7 PM
Venue: Ramanujan Hall
Speaker: Surajit Pal
Abstract: In this talk, we will state the control ability of the control system, and then we will give the observability inequality, which is equivalent to exact controllability. Also, we will state the equivalent condition for another type of control.
Time: 5 PM–6 PM
Venue: Ramanujan Hall
Speaker: Om Milind Joglekar
[This is continuation of the previous talk.]
Time: 4 PM–5 PM
Venue: Ramanujan Hall
Speaker: Om Milind Joglekar
Abstract: In 1900, Frobenius discovered a remarkable generating function for the irreducible characters of the symmetric group Sn. It was well known that by lifting the trivial character of the subgroup Sp_1 × ... × Sp_n (associated with a partition p of n) to a compound character φp of Sn, the generating function of φp restricted to some conjugacy class λ, yields the power sum symmetric function indexed by λ. Multiplying this by the Vandermonde determinant, Frobenius ingeniously derived the generating function for the irreducible characters of Sn. This seminar will explore his elegant construction, highlighting its deep connections between representation theory and symmetric functions.
Time: 4 PM–5 PM
Venue: Ramanujan Hall
Speaker: Lal Bahadur Sahu
Abstract: I will state one of the Peter–Weyl theorem and see it's few applications on representation theory of compact Lie groups.
Time: 4 PM–5 PM
Venue: Ramanujan Hall
Speaker: Ramdas Omkar Prasad
Abstract: The Combinatorial Nullstellensatz, a clever algebraic tool by Noga Alon, is a fundamental theorem linking algebra and combinatorics. This talk will focus on presenting the theorem's statement, key conditions, and underlying algebraic ideas, with a central emphasis on understanding its proof. By walking through the details of the proof, we will explore how this result provides insights into the connection between polynomials and combinatorial structures, highlighting its theoretical significance.
Time: 4 PM–5 PM
Venue: Ramanujan Hall
Speaker: Amal Das
Abstract: In this talk I will introduce Leray-Schauder degree theory and its immediate application in nonlinear problems, in particular existence of solution for semilinear PDE.
Time: 4 PM–5 PM
Venue: Ramanujan Hall